Marion has 30% as many buttons as Zara. Zara has 110% as many buttons as Kimberly. If Zara gives 25 buttons to Kimberly, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Marion	Zara	Kimberly
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

The number of buttons that Marion has is repeated.  Make the number of buttons that Marion has the same. LCM of 10 and 11 is 110.

	Zara	Kimberly	Total
Before	110 u	100 u	210 u
Change	- 5 u	+ 5 u
After	105 u	105 u	210 u

Total number of buttons that Zara and Kimberly have
= 110 u + 100 u
= 210 u

After Zara gives to Kimberly, both of them will have the same number of buttons. 

The total number of buttons that Zara and Kimberly have remains unchanged.

Number of buttons that each of them will have
= 210 u ÷ 2
= 105 u

Number of buttons that Zara gives to Kimberly
= 110 u - 105 u
= 5 u

5 u = 25

1 u = 25 ÷ 5 = 5

Total number of buttons that three of them have
= 210 u + 33 u
= 243 u

Average number of buttons that each of them have
= 243 u ÷ 3
= 81 u
= 81 x 5
= 405

Answer(s): 405